Decoupled Planning for Multiple Omega-Regular Objectives

2026-05-13

AI Summary

This work addresses the problem of coordinating multiple agents in a decentralized setting, where each agent must plan a path satisfying its own ω-regular objective while collectively generating a globally correct execution. To this end, the authors propose a decoupled framework in which agents synthesize local strategies based solely on their individual objectives, and a scheduler—agnostic to both the system graph and agent goals—dynamically composes these into a complete path. Theoretical analysis reveals that strongly fair deterministic schedulers are insufficient to guarantee correctness. Accordingly, tailored coordination mechanisms are introduced: a synchronization protocol for safety objectives and a prior agreement scheme for non-safety objectives. The study further characterizes the minimal coordination information required for key ω-regular subclasses: finite-memory strategies suffice for Büchi objectives without communication; co-Büchi objectives require access to scheduling history; and Parity objectives additionally necessitate knowledge of scheduler identity to ensure joint satisfaction.

Abstract

We study the problem of generating paths on a graph that satisfy a collection of ω-regular objectives. We propose a decoupled framework in which each objective is assigned to an independent agent that selects a local policy, while a scheduler -- oblivious to the graph and objective -- dynamically composes these policies into a single path. We ask when such a composition satisfies all objectives, assuming their conjunction is realizable. The framework enables modular policy design but raises fundamental compositional challenges. We show that even extremely fair deterministic schedulers do not ensure correctness, and that stochastic schedulers, while necessary, are insufficient without coordination. For safety objectives, we demonstrate that fully decentralized implementations are impossible, and we introduce a protocol for synchronizing on maximal safe actions. For non-safety objectives, we introduce conventions -- simple, a priori restrictions agreed upon before the graph or objectives are revealed -- that guarantee satisfaction of all objectives when followed by all agents. We characterize minimally restrictive conventions for major subclasses of ω-regular objectives. In particular, Büchi objectives admit universal composition of finite-memory policies without scheduler communication; co-Büchi objectives require only knowledge of whether the agent was scheduled; and parity objectives additionally require knowledge of which agent was scheduled.

Problem

• omega-regular objectives
• decentralized planning
• path synthesis
• multi-agent coordination
• temporal logic

Innovation

• decoupled planning
• omega-regular objectives
• compositional synthesis
• multi-agent coordination
• scheduler conventions